I already replied to most of this on the Steam forums, but basically:
Tried lowering the res; no dice.
The drivers are up to date and the specs are fine.
I'm on a single display setup.
I did send an email to your tech support. I'd attach my DXDiag here, but GOG forums don't want me to for some reason.
alxltz: That is definitely curious that the issue is only occurring in BR1 for you, though, as both games use the same tool to play back the cutscenes. We can ask Terminal to take a look if you can send us your configuration info. We have also seen some configurations where the GOG Galaxy overlay can conflict with the game's rendering to cause flickering, so it might be worth trying to disable the GOG overlay in Galaxy via the Settings button to the right of the Play button when the game is selected, then Manage Installation > Configure.
I don't use the GOG Galaxy overlay and I did run the game without it and directly from the .exe many times, so that's not it.
EDIT: It seems that I can't even use the GOG Galaxy overlay in BR1TC. It does work in BR2TC though, and once again, there's no flicker.